Least Common Multiple

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Find the *Least Common Multiple* (LCM) of the numbers 2700 and 420.

**Answer**

$2700=({2}^{2})({3}^{3})({5}^{2})$

$420=({2}^{2})(3)(5)(7)$

The LCM of 2700 and 420 is the product of the largest powers of each prime factor in both.

Thus the LCM of 2700 and 420

$=({2}^{2})({3}^{3})({5}^{2})(7)$

$=18900$